The present study is concerned with the application of immersed interface method to simulate flow with elastic membrane, which causes a discontinuous transport property. The numerical framework is based on the finite volume approach with the projection method. First, this method is conducted to the convection-diffusion equation to examine the numerical accuracy of this method. It was discovered that by appropriately differentiating the source term, second order accuracy can be achieved. The scheme is further applied to simulate stokes equation with the tangential force problem. The numerical result shows that the deficiency of the finite volume approach, which degrades the order of accuracy the method. Finally, the flows with single and multiple moving membranes are simulated to examine the applicability of this method under a complex environment.

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